274
Quarterly Bulletin 2008 Q3
Market expectations of future
Bank Rate
By Michael Joyce and Andrew Meldrum of the Bank’s Monetary Instruments and Markets Division.
This article discusses various financial instruments that can be used to infer the Bank Rate
expectations of financial market participants and examines how well these measures have predicted
Bank Rate in the past. It also examines the role of model-based and survey information in assessing
financial market Bank Rate expectations. The article suggests that it is important to adjust market
interest rates for credit, liquidity and term premia when inferring expectations. It finds that credit
and liquidity premia can largely be accounted for, either through the choice of financial instrument
or by making some simple adjustments. Although recent advances in term structure modelling
provide some useful techniques for adjusting for term premia, there is considerable uncertainty
about how robust they are. It remains prudent therefore not to rely on any one measure and
instead to use a variety of methods and information for this purpose.
Introduction
The Bank of England’s Monetary Policy Committee (MPC) is
interested in what financial market participants think will
happen to Bank Rate, the UK policy rate, for a variety of
reasons. Most obviously, investors’ interest rate expectations
affect the lending and borrowing rates facing firms and
consumers and so play an important role in the transmission
mechanism of monetary policy to the real economy.
Monetary policy makers naturally want to know how their
decisions and communications are affecting these
expectations. Moreover, market expectations may themselves
contain useful information about investors’ perceptions of
current and future economic developments, which
policymakers might want to incorporate into their own view
of the outlook. In addition, the MPC conditions its inflation
and output projections published in the Inflation Report on a
profile for market interest rate expectations and therefore
needs a method of producing this profile that delivers
consistent and plausible results.
interest rates, particularly over more distant future periods
ahead, may embody term premia — the compensation
investors require for the risk of future interest rate changes —
which will further complicate their relationship with policy rate
expectations.
As Chart 1 illustrates, there can sometimes be material
differences between different market interest rates, as well as
between market interest rates and the survey-measured
expectations of professional forecasters. These differences
have been particularly marked since the onset of the current
turmoil in financial markets, which has accompanied large
Chart 1 Forward interest rates and survey expectations
of Bank Rate a year ahead
Per cent
Unsecured interbank lending rates(a)
7.0
6.5
6.0
5.5
The interest rates on a variety of financial market instruments
will be closely related to the current level and future
expectations of Bank Rate and so can provide indications of
those expectations. However, different instruments vary in
terms of their credit quality (default risk) and liquidity (the
ease with which investors can take or close positions in the
market for the instrument). The resulting credit and liquidity
risk premia required by investors in compensation may drive
the interest rates associated with these instruments away
from genuine Bank Rate expectations. Moreover, all market
5.0
Estimated default
risk-free rates(b)
4.5
4.0
Survey of professional economists(c)
2005
06
07
08
3.5
0.0
Sources: Bank of England, Bloomberg and Reuters.
(a) Derived from Libor rates and derivative instruments that settle on Libor.
(b) Calculated to be consistent with the methods used to produce the market profiles of interest
rates published in previous Inflation Reports (see discussion in main text).
(c) The Reuters survey of City forecasts closest to one year ahead.
Research and analysis Market expectations of future Bank Rate
increases in the credit and liquidity premia associated with
some instruments. But the general issue of how best to take
account of risk premia in deriving financial market
expectations of Bank Rate — the focus of this article — is an
important question that always faces the MPC and others
monitoring market expectations. (The ‘Markets and
operations’ article in this Quarterly Bulletin contains a more
detailed discussion of recent developments in sterling
short-term interest rates.)
This article provides an overview of the available financial
market instruments that can be used to infer Bank Rate
expectations and evaluates them in terms of their ability to
predict Bank Rate over the period predating the onset of the
market turbulence last summer. It goes on to examine ways of
adjusting market rates for term premia and the use of survey
information on expectations. The article suggests that credit
and liquidity premia can be largely accounted for, either
through the choice of financial instrument or by applying
some simple adjustments. This is consistent with the
approach taken for producing a profile for market interest
rate expectations to condition the Inflation Report
projections. Adjusting for term premia remains more
challenging. Though recent advances in term structure
modelling can provide some useful techniques for this
purpose, there is still considerable uncertainty about the
robustness of these methods.(1)
Market measures of Bank Rate expectations
The MPC sets Bank Rate, the official rate paid on commercial
bank reserves at the Bank of England. As explained above,
while market participants’ expectations of the future path of
Bank Rate cannot be observed directly, the interest rates on a
variety of financial market instruments can be used to indicate
market expectations. The associated interest rates at different
maturities can be used to infer so-called forward interest rates
— the interest rates available now, at which people can borrow
or lend over some future period. If there were no credit,
liquidity and term premia, these forward market interest rates
would provide a measure of the implied market expectations
of future policy rates at different future horizons.(2) But even if
there are premia, provided they remain reasonably constant,
changes in market rates may still provide useful information
on changes in Bank Rate expectations.
The available instruments that can be used for this purpose
can be broadly grouped into three categories:
(1) measures based on government bonds and repo (secured)
interbank lending rates;
(2) measures based on Libor (unsecured) interbank lending
rates; and
(3) measures based on SONIA (unsecured) overnight
interbank lending rates.
275
(1) Government bonds and secured lending rates
A conventional UK government bond, or ‘gilt’, is a promise by
the government to pay the holder a fixed cash payment
(coupon) every six months until the maturity date, at which
point the holder receives the final coupon payment and the
principal.
Since gilts are issued by the UK government, they can be
regarded as free of credit risk, and therefore might be thought
of as an obvious instrument to use for inferring future policy
rate expectations. However, one difficulty of using them for
this purpose is that there are generally few government bonds
with short maturities.(3)
General collateral (GC) repo contracts are a method of
short-term borrowing that involves the temporary exchange of
cash and gilts between two parties. Since the lender of funds
receives high-quality assets as collateral, it is protected if the
borrower were to default; hence this is a form of secured
lending. GC repo rates should therefore, in principle, reflect
only minimal credit risk premia. They may, however, be
affected by liquidity conditions in money markets and, as a
result, include liquidity risk premia.
(2) Libor lending rates
An interbank loan is a cash loan where the borrower receives
an agreed amount of money at an agreed interest rate. The
loan is unsecured, as the lender does not receive collateral as
protection against default by the borrower.
The London interbank offered rate (Libor) provides a measure
of the interest rate at which banks can raise unsecured funds
from other financial institutions. The British Bankers’
Association publishes sterling Libor for maturities ranging from
overnight to one year. The financial institutions that are part
of the Libor panel are long-established creditworthy
institutions, but the loans are unsecured and so carry some
possibility of default. The interest rates required by the lender
will reflect this repayment risk, so Libor rates include credit
premia relative to default risk-free rates. Furthermore, Libor
rates will also be affected by liquidity conditions in money
markets and so will also contain liquidity risk premia.
A number of other instruments are linked to future values of
Libor, including sterling short-term interest rate futures
contracts, forward rate agreements (FRAs) and Libor swaps.
Since they are linked to three or six-month Libor, their
associated interest rates also contain credit and liquidity
premia.
(1) Joyce, Sorensen and Weeken (2008) discuss some of these methods in more detail.
(2) Such an inference also requires that financial markets operate efficiently and without
frictions and that investors have no a priori reasons for investing at particular horizons
(‘preferred habitats’).
(3) This article does not examine Treasury bills, which are government bonds with a year
or less to maturity when issued, because the secondary market for these instruments
has not been sufficiently liquid.
276
Quarterly Bulletin 2008 Q3
(3) SONIA lending rates
on the Bank of England website).(2) For conciseness, this article
refers to the interest rate profile constructed for the purposes
of conditioning the Inflation Report projections as the ‘adjusted
BLC’.
An overnight index swap (OIS) is a contract that involves the
exchange at maturity of a payment linked to a predefined
interest rate for one linked to the compounded overnight
interest rate that has prevailed over the life of the contract.
The relevant overnight rate for sterling contracts is the sterling
overnight index average (SONIA), which is calculated by the
Wholesale Market Brokers’ Association. As SONIA is an
overnight rate, and credit risk in overnight transactions should
generally be small compared with longer-maturity deals, it is
usually close to Bank Rate. The OIS contracts themselves are
structured so that they involve minimal counterparty risk, so
OIS rates should not reflect material credit risk premia. Hence
the expected path of SONIA embodied in OIS rates should be
closely related to that of Bank Rate.
The volume of trading in the OIS market has risen rapidly over
the past few years. One recent innovation has been the
introduction of so-called meeting-to-meeting swaps that are
aligned with future MPC meeting dates. The box at the end of
this article discusses the different types of OIS contract and
the ways in which their associated interest rates can be used to
compute forward rates.
Yield curves
One difficulty when interpreting the quoted interest rates for
the instruments discussed above is that they do not all refer to
the same future periods. There may also be gaps between
those periods, so it is not straightforward to make inferences
about Bank Rate expectations at all future horizons. The Bank
of England therefore uses several financial market instruments
to estimate smooth and continuous forward yield curves for
the United Kingdom. These curves show the interest rates for
future periods that are implied by current market prices.
The Bank of England estimates two main kinds of yield curve,
which are also made publicly available on its website.(1) One —
called the government liability curve (GLC) — is based on the
interest rates on UK government bonds, and on GC repo rates
at horizons of up to one year. The other — called the bank
liability curve (BLC) — is based on Libor interest rates and
market rates on derivative instruments linked to Libor:
short-term interest rate futures, FRAs and Libor swaps.
The market profile used for the MPC’s Inflation Report
projections
The inflation and GDP projections published in the quarterly
Inflation Report are conditioned on a path for official interest
rates implied by market yields. For these purposes,
information from different instruments and yield curves is
combined together. Currently this profile is based on OIS rates
at horizons out to a year and BLC forward rates adjusted for
credit and liquidity premia at longer horizons (the August
2008 Inflation Report states which instruments were used;
further details of the current and earlier methods are provided
How well do market interest rates predict
Bank Rate?
Given the large number of instruments that can potentially be
used to infer Bank Rate expectations, it is desirable to have a
means of choosing between them. One approach is to
examine how well they have predicted Bank Rate over a
reasonably long period in the past. While superior predictive
content does not necessarily guarantee a measure is
representative of market expectations, it seems reasonable to
assume that those instruments that have more accurately
predicted Bank Rate are less likely to have been affected by
other factors and to place correspondingly more weight on
them.
In order to carry out a comparative analysis, it is necessary to
construct comparable forward rates from each instrument
which can then be compared to Bank Rate outturns over the
same period. To include as many instruments as possible, the
forward rates used refer to three-month periods. The range of
forecast horizons considered in the empirical analysis went up
to two years ahead (although it varied across instruments
depending on the maturities actively traded in each market).
To test the predictive content of the derived forward rates, the
change in Bank Rate from the current period to each future
horizon was regressed onto the change in rates implied by the
appropriate forward rate. More specifically, this meant
running the following regression for each curve or instrument
being considered:
(
)
∆BRt ,t + h = α + β ft ,t + h − BRt + ε t
where ∆BRt,t+h is the change in Bank Rate between time t and
t+h, ft,t+h is the forward rate from each measure being assessed
at horizon h, BRt is the Bank Rate at time t, α and β are
respectively the constant and slope coefficients from the
regression and εt is an error term.(3)
If forward rates are unbiased estimates of future policy rates
then the α and β coefficients would be expected to be zero
and one respectively. More realistically, if term, credit and
(1) The method used to produce both these curves is a smoothed cubic spline technique
and is explained by Anderson and Sleath (1999, 2001). Its application to bank liability
instruments is described by Brooke, Cooper and Scholtes (2000). Estimates can be
downloaded from: www.bankofengland.co.uk/statistics/yieldcurve/index.htm.
(2) www.bankofengland.co.uk/publications/inflationreport/conditioning_path.htm.
(3) Gurkaynak, Sack and Swanson (2007) perform a similar analysis using US financial
market instruments.
Research and analysis Market expectations of future Bank Rate
Chart 2 Forecast regression results: explanatory power
Adjusted R-squared
GLC
GC repo
Libor
OIS
BLC
Adjusted BLC
Futures
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
3
6
9
12
15
Horizon (months)
18
21
0.0
24
Source: Bank calculations.
Chart 3 Forecast regression results: value of constant
term, α
α
GLC
GC repo
Libor
OIS
0.0
–
BLC
Adjusted BLC
Futures
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0
3
6
9
12
15
Horizon (months)
18
21
0.8
24
Source: Bank calculations.
Chart 4 Forecast regression results: value of slope
coefficient, β
β
GLC
GC repo
Libor
OIS
BLC
Adjusted BLC
Futures
277
liquidity risk premia are different from zero on average, this
would be reflected in the value of the constant term (α). And
if premia vary over time, the slope coefficient (β) would be
expected to be different from one because not all forward
rate movements will reflect changes in expectations of future
Bank Rate.
Charts 2–4 plot the adjusted R-squared (a measure of how
well the regressions explain the data) and the α and β
coefficients by horizon for each of the instruments and curves
examined over the longest sample periods available since
October 1992, when the United Kingdom first adopted an
explicit inflation target, to March 2007.(1) For some
instruments the sample period is much shorter than for others,
although the results shown hold qualitatively if the regressions
are run over common sample periods.
Perhaps the most striking result to emerge is how well some of
the instruments and curves do in forecasting future interest
changes, particularly at shorter horizons (Chart 2).(2) For
example, market forward rates can explain as much as 60% of
the variation in Bank Rate at the three-month horizon. In fact,
other analysis suggests that the predictive power of all the
instruments and curves beats the common benchmark of
assuming there is no change in rates going forward (interest
rates follow a ‘random walk’), though, as might have been
expected, the explanatory power of the instruments and
curves tends to fall as the forecasting horizon lengthens.
No instrument or curve clearly dominates all the others
consistently across all maturities. However, the clearest
finding is that forward rates derived from instruments that are
least likely to embody material credit and liquidity risk premia
tend to do better in the forecasting regressions; and, of the
yield curves that extend to longer horizons, the government
curve and the adjusted BLC constructed in the same way as
the market profile used for the Inflation Report projections
tend to outperform the BLC. It is difficult to discriminate
between the other instruments, but that is perhaps not
surprising if the same expectations are consistently reflected in
different instruments.
1.2
1.0
0.8
0.6
0.4
Turning to the parameter estimates, in all the forecasting
regressions, the constant term (though not always statistically
significant) takes a negative sign, which increases in absolute
size with maturity (Chart 3). The implication that forward
rates have tended to overpredict policy rate outturns,
irrespective of whether the related instruments are likely to
embody material credit and liquidity risk premia, is consistent
with there being a positive term premium on average,
0.2
0
3
6
Source: Bank calculations.
9
12
15
Horizon (months)
18
21
24
0.0
(1) This analysis draws extensively on Joyce, Relleen and Sorensen (2008). The sample
period predates the turbulence in financial markets that started in Summer 2007,
when credit and liquidity premia increased sharply.
(2) This is consistent with other research (for example, Lildholdt and Vila Wetherilt
(2004)) that suggests that the predictability of UK policy rates improved notably after
the introduction of inflation targeting in the United Kingdom.
278
Quarterly Bulletin 2008 Q3
particularly at the longer horizons. Chart 4 shows that the β
coefficient is positive throughout (and tests suggest it is often
statistically significant), though less than one and generally
decreasing in maturity. Though the pattern varies slightly
according to the instrument/curve and sample period, on the
whole, formal statistical tests cannot reject β being equal to
one at short horizons out to a year, but at longer horizons this
hypothesis tends to be rejected.
Of the available surveys of Bank Rate expectations, the most
suitable is probably the Reuters survey of professional City
economists, which has run in some form since the late
1990s.(1) While the precise format has varied, in recent
months the survey has asked around 70 economists every
month for their expectations of future Bank Rate at the end of
each quarter, up to about 18 months ahead. Chart 5 shows
how Reuters survey expectations for Bank Rate at the end of
successive calendar years compare with comparable forward
rates. The surveys and forward rates tend to move in a broadly
similar fashion, although there have sometimes been material
gaps between the two. It is not obvious, however, whether
these gaps are caused by the presence of term premia in
forward rates or any of the caveats related to surveys listed
above. In conclusion, therefore, while surveys can provide a
useful source of information on Bank Rate expectations, they
do not circumvent the need to interpret market interest rates.
Nevertheless, as will be discussed further below, it is possible
to use modelling methods that incorporate survey information
as a noisy signal of expectations.
The evidence on the way the α and β coefficients vary with
horizon is consistent with term premia becoming important at
horizons of a year and beyond, which potentially obscures the
information in market rates about future policy rate
expectations.
Accounting for term premia
The empirical analysis described in the previous section
suggests that forward rates that are less likely to embody
significant credit and liquidity premia, or that have been
adjusted to take account of such premia in the same way as
the market profile used for the Inflation Report projections,
have provided the more reliable forecasts of Bank Rate. But all
financial instruments have provided biased estimates of future
Bank Rate movements, at least beyond horizons of a year
ahead. Although other causes are possible (including that
expectations were persistently higher than outturns over the
estimation period), these results are consistent with the
presence of time-varying term premia, raising the issue of how
best to take these premia into account when interpreting
forward rates.
Chart 5 End-year Reuters surveys and GLC forward
rates(a)
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Per cent
7.0
6.5
6.0
5.5
5.0
Before discussing how this can be done, however, it is worth
asking whether the issue can be avoided entirely by relying on
survey information on policy rate expectations.
4.5
4.0
3.5
3.0
Survey measures
Surveys of Bank Rate expectations provide measures that do
not reflect any credit, liquidity or term premia. However, one
difficulty with using survey information is that respondents —
who are typically professional economists — may have
expectations that are not representative of market
participants. There are also other caveats with surveys,
including the fact that respondents may take time to revise
their reported views and the fact that some surveys are carried
out over a period of several days rather than referring to a
specific point in time. Another potential difficulty is that
surveys may capture the Bank Rate thought most likely to
occur (the modal expectation) rather than the average (mean)
expectation implicit in market interest rates. This difference
can matter, for example, when the perceived balance of risks
around the expected future path of Bank Rate is particularly
skewed one way or another. In addition to these caveats,
surveys are also not typically available at a sufficiently high
frequency for those monitoring financial markets on a
day-to-day basis.
2.5
1999 2000
01
02
03
04
05
06
07
08
2.0
0.0
Sources: Bank of England, Bloomberg and Reuters.
(a) Solid lines show GLC forward rates. Diamonds show survey expectations.
Empirical models
One way of taking term premia into account when interpreting
market interest rates (already adjusted for credit and liquidity
premia) is to use an empirical interest rate model. A widely
used approach for estimating term premia is to use a so-called
‘affine term structure model’.(2) There are many variants of
(1) Similar surveys are conducted by Bloomberg and HM Treasury. The Bank of England
also conducts a quarterly poll of Bank Rate expectations, which is published in the
Inflation Report.
(2) There are a variety of other possible ways of modelling term premia. For example,
Peacock (2004) models survey-based term premia in terms of other financial market
indicators. For a review and assessment of different methods, see Joyce, Relleen and
Sorensen (2008) and Kim and Orphanides (2007).
Research and analysis Market expectations of future Bank Rate
these models;(1) but central to all these variants is an
assumption that bond prices are set in such a way as to
eliminate arbitrage opportunities, so that there are no risk-free
profits to be made by trading combinations of bonds. The
assumption of no arbitrage ensures that the models price risk
consistently for all bonds.
279
Chart 6 Model-based estimate of Bank Rate
expectations two years ahead
Per cent
7.5
7.0
Adjusted BLC forward rate
6.5
6.0
In many models of this type, including the one discussed in the
next section, bond prices, interest rate expectations and term
premia are all driven by a small set of unobserved ‘factors’.
These factors are essentially combinations of interest rates of
different maturities, where the weight attached to each
interest rate is estimated from the data. This means that
expectations of future interest rates can be thought of as being
the forecasts from regressions of interest rates on their past
values (where those past values are weighted together to form
factors), and where all the parameters of the model are
restricted to be consistent with the assumption of no
arbitrage. The model’s estimate of the term premium is then
the difference between the forward rate and the model’s
estimate of the expected future short rate.
5.5
5.0
4.5
4.0
3.5
Expected Bank Rate estimated by model
2000
01
02
03
04
05
06
07
3.0
0.0
08
Source: Bank calculations.
Combining information from interest rates and
surveys
Chart 7 shows the estimated average term premium over
different horizons, as well as the ranges and interquartile
ranges of those premia over the same period. The average
premium is positive for rates further than about six months
ahead and rises for longer horizons. There is also substantial
variation in the premium over time. Both of these findings are
in line with the regressions presented in the previous section.
Some recent work at the Bank has applied the affine modelling
approach to estimating the path of Bank Rate over the short to
medium-term horizons discussed in this article.
Chart 7 Estimated term premia since April 2000
The forward interest rates used to estimate the affine model
are consistent with the market profiles of forward rates used to
condition the MPC’s Inflation Report projections and therefore
should not reflect material credit or liquidity premia. The
model also incorporates information from the Reuters survey
of economists’ expectations of Bank Rate as close as possible
to a year ahead. It interprets the survey information as a noisy
signal of market expectations, putting greater or lesser weight
on the surveys according to how they have tended to comove
with interest rates in the past. For example, if surveys
provided especially good forecasts of interest rates when the
yield curve took a particular shape in the past, the affine model
would put more weight on surveys if those circumstances
arose again. The expectations of Bank Rate implied by this
particular affine model can therefore be thought of as being
generated as the forecast from a regression of short-term
interest rates on both interest rates of longer maturities and
the surveys.
Evidence on time-varying term premia
Chart 6 shows the adjusted BLC forward rates used in the
affine model alongside estimated Bank Rate expectations two
years ahead — ie stripping out term premia — since
April 2000. Estimated expectations of Bank Rate are broadly
similar to forward rates over most of the sample, although
there are periods where they have deviated substantially, with
the largest differences being as much as 80 basis points.
Range
Interquartile range
Mean
Per cent
1.0
0.8
0.6
0.4
0.2
+
0.0
–
0.2
0.4
0
1
Years ahead
2
0.6
Source: Bank calculations.
In general, economic theory would suggest that the absolute
size of the term premium — the compensation investors
demand for the risk surrounding future interest rates — will
depend on how uncertain investors are about the future path
of interest rates and the wider macroeconomic outlook; and
on how much investors care about their exposure to risk.
(1) Joyce, Sorensen and Weeken (2008) discuss some different types of term structure
model, including the affine model framework used in this article.
280
Quarterly Bulletin 2008 Q3
But term premia need not always be positive, as this will
depend on how interest rates vary with the value investors
place on high returns. When interest rates rise, this means
that the price of, and hence returns on, assets such as bonds
falls. So if interest rates tend to turn out particularly high
during ‘bad times’, this means that bond returns will be low at
the time when investors would most value greater returns.
Investors in bonds would therefore require a higher rate of
return — a positive term premium — to compensate them for
this uncertainty. High interest rates might tend to be
associated with low economic growth following an adverse
shock to the supply capacity of the economy. So the positive
average term premium might suggest that, on average over
the period, investors were more concerned about shocks to
supply than to demand.
models may produce different results. Moreover, recent
research in the Bank suggests that models that fit the term
structure well in-sample do not always fit well outside the
sample period over which they are estimated.(1) As a result, no
mechanical adjustments for term premia are applied when
estimating a market profile of forward interest rates for the
purposes of conditioning the Inflation Report projections.
Instead, the MPC monitors a number of different estimates of
expectations — derived from both term structure models and
surveys — when interpreting those forward interest rates.
Developments since the beginning of 2008 demonstrate the
importance of taking likely movements in term premia into
account when interpreting forward interest rates. Chart 8
shows the one year ahead forward rate used in the affine
model, alongside the model’s estimated expectations of Bank
Rate. This shows that market forward rates rose by around
1.5 percentage points between early May and the middle of
June 2008, before falling by approximately the same amount
by the end of August. In contrast, while the affine
model-based expectations of Bank Rate moved in the same
direction as forward interest rates, they did so by smaller
amounts. This implies that the estimated term premium
changed from negative (ie forward rates below expectations)
to positive and back over the period shown in the chart.
According to the economic theory described in the previous
paragraphs, these changes in sign could be consistent with
changes to the relative weights investors attached to shocks to
supply and demand.
Chart 8 Model-based measure of Bank Rate
expectations one year ahead
Per cent
6.0
5.8
Conclusions
This article discussed the various instruments that can be used
to measure the Bank Rate expectations of financial market
participants and assessed how well they had predicted Bank
Rate in the past. One of the main findings was that the
forward rates that are least likely to embody significant credit
and liquidity premia, or that have been adjusted to take
account of such premia, have provided the most reliable
forecasts. This supports the MPC’s recent approach to the
calculation of market profiles of interest rates to condition its
Inflation Report projections: these profiles have been based on
combinations of forward rates derived from instruments that
are close to default risk-free (secured interbank lending rates
and overnight index swaps) and Libor-based instruments
adjusted to account for credit and liquidity premia.
The other main finding was that the available forward rates at
horizons of a year and beyond have provided biased forecasts
of Bank Rate expectations, irrespective of whether they
embody significant credit and liquidity premia. This result
could be consistent with the existence of additional,
time-varying term premia. One way of potentially avoiding
term premia is to focus on the expectations from surveys. But
the available surveys may not be representative of market
participants and have their own limitations. Instead, the
article developed an empirical term structure model that
incorporated both market interest rates and survey
information as a means of estimating market expectations.
5.6
5.4
5.2
5.0
Expected Bank Rate
estimated by model
4.8
4.6
4.4
Adjusted BLC forward rate
4.2
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
4.0
0.0
Source: Bank calculations.
These results should be interpreted with caution, however,
since they are specific to one particular model; different
The model-based estimates provide a useful tool for assessing
the information in market rates and surveys. However, given
the uncertainties involved it would seem prudent to monitor
alternative measures of expectations and attempt to
understand what is driving the differences between them,
rather than relying exclusively on any one particular method to
adjust mechanically for term premia. This is consistent with
the MPC’s convention of conditioning the Inflation Report
projections on a market profile of forward interest rates
unadjusted for term premia. But this remains an active area of
research at the Bank and elsewhere.
(1) This is discussed in more detail by Joyce, Relleen and Sorensen (2008).
Research and analysis Market expectations of future Bank Rate
Overnight index swaps
One class of instrument that can be used to calculate forward
interest rates is that of ‘overnight index swaps’ (OIS). As
explained in the main text of the article, sterling contracts
settle on the sterling overnight index average (SONIA) and
involve the exchange of a payment linked to a fixed interest
rate for one linked to the compounded SONIA rates over the
lifetime of the contract. Both legs are based on the same
notional principal. There are two types of OIS contracts. This
box explains in turn how they can be used to estimate forward
interest rates.
continuous yield curves to spot OIS rates using the same
techniques that are applied to other instruments discussed in
this article. The blue line in Chart A shows an example of a
forward curve estimated in this way.
Chart A Forward yield curves derived from OIS,
29 August 2008(a)
Per cent
5.0
Meeting-to-meeting
step-chart
OIS forward curve estimated
using cubic splines
4.8
4.6
‘Spot’ OIS contracts refer to different periods ending in the
future. These contracts are most widely used at horizons up to
a year ahead but there has been increasing activity at longer
horizons in recent months.
This technique is only likely to be appropriate at very short
horizons as it assumes that there are no term premia in
forward interest rates. An alternative technique, which does
not depend on any assumptions about term premia is to fit
5.2
Conventional step-chart
Spot OIS
The quoted OIS rate (the fixed leg of the swap) should be
equal to the compounded forward interest rates relating to
each day over the contract. This means that spot OIS rates can
be used to back-out implied forward rates. One method of
doing this involves the assumption that forward rates should
be constant between successive MPC decision dates, which
allows the estimation of a piecewise constant forward curve
(a ‘conventional step-chart’) such as that shown by the pink
line in Chart A. A description of this technique is provided in
Bank of England (2005).
281
4.4
4.2
Aug.
Nov.
Feb.
2008
May
4.0
0.0
09
Sources: Bank of England and Bloomberg.
(a) Step-charts shown over period for which future MPC meeting dates were published.
Forward-starting OIS
‘Forward-starting’ or ‘meeting-to-meeting’ OIS rates are those
available today but referring to periods that start and end on
future dates. In the sterling market, quotes are available for
periods between future MPC meeting dates. Activity in these
contracts is most liquid at horizons up to around six months
ahead. The green line in Chart A shows an example of such a
‘meeting-to-meeting step-chart’, which on this particular date
was close to the conventional step-chart.
282
Quarterly Bulletin 2008 Q3
References
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nominal yield curves’, Bank of England Quarterly Bulletin, Vol. 39,
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Joyce, M, Relleen, J and Sorensen, S (2008), ‘Measuring monetary
policy expectations from financial market instruments’, forthcoming
Bank of England Working Paper.
Anderson, N and Sleath, J (2001), ‘New estimates of the UK real and
nominal yield curves’, Bank of England Working Paper no. 126.
Joyce, M, Sorensen, S and Weeken, O (2008), ‘Recent advances in
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